HK1060431B - Method and device for processing time-discrete audio sampled values - Google Patents

Description

The present invention relates to audio coding and in particular to processes and devices for processing time-discrete audio sample values to obtain integer output values.

Modern audio coding techniques, such as MPEG Layer3 (MP3) or MPEG AAC, use transformations such as the so-called modified discrete cosine transform (MDCT) to obtain a block-by-block frequency representation of an audio signal. Such an audio coder usually receives a stream of time-discrete audio sound values. The stream of audio sound values is windowset to obtain a window block of, for example, 1024 or 2048 window sound values.

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In the audio decoder, the bitstream is divided into encoded quantized spectral values and side information by means of a bitstream demultiplexer. The entropy-encoded quantized spectral values are first entropy-decoded to obtain the quantized spectral values. The quantized spectral values are then inverse-quantized to obtain decoded spectral values that have quantization noise, but which is below the psychoacoustic masking threshold and will therefore be inaudible. These spectral values are then converted into a time representation by means of a synthesis filter bank to obtain discrete decoded audio values.

To achieve good frequency selectivity, modern audio encoders typically use block overlap. One such case is shown in Fig. 4a. For example, 2048 time-discrete audio samples are first taken and displayed by means of a device 402. The window embodying device 402 has a window length of 2N samples and outputs a block of 2N window samples. To achieve window overlap, a device 404 is used, which is only visually separated from device 402 for overview purposes in Fig. 4a, a second block of 2N window samples is displayed.Err1:Expecting ',' delimiter: line 1 column 177 (char 176)

In the decoder, the N spectral values of the first window, as shown in Fig. 4b, are fed to a device 412 performing an inverse modified discrete cosine transformation, and the N spectral values of the second window are fed to a device 414 performing an inverse modified discrete cosine transformation. Both the device 412 and the device 414 provide 2N sampling values for the first window and 2N sampling values for the second window, respectively.

In a device 416 designated in Fig. 4b with TDAC (TDAC = Time Domain Aliasing Cancellation), the overlap between the two windows is taken into account. In particular, a scan value y1 from the second half of the first window, i.e. with an index N+k, is added to a scan value y2 from the first half of the second window, i.e. with an index k, so that the output, i.e. the decoder, has N decoded time scan values.

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If the window function implemented by the device 402 or 404 is denoted by w(k), where the index k is the time index, the condition must be fulfilled that the window weight w(k) squared plus the window weight w(N+k squared is 1 together, where k runs from 0 to N-1.

The disadvantage of the window method with subsequent MDCT function described in Fig. 4a is that the window is obtained by multiplying a time-discrete sampling value by a floating point number when thinking of a sine window, since the sine of an angle between 0 and 180 degrees apart from the angle 90 degrees does not give an integer.

Therefore, even if no psychoacoustic coding is used, i.e. if lossless coding is to be achieved, quantization at the output of the devices 408 and 410 is necessary to perform a reasonably manageable entropy coding.

Thus, if known transformations, as in Fig. 4a, are to be used for lossless audio coding, either a very fine quantization must be used to negate the resulting error due to rounding of the floating point numbers, or the error signal must additionally be coded, for example, in time.

Furthermore, digital signal processors usually have an accumulator with a larger word length than the usual operator length to avoid too many rounding operations. Using fast algorithms to implement a filter bank typically results in the need to store intermediate results to be used in later steps. The intermediate results need to be rounded to operator accuracy or split into two storage operations. Typically, the error rates of several processing steps accumulate.

Both too fine quantization and the additional coding of the error signal as an alternative result in an encoder with increased computational effort and complexity, and thus also in a correspondingly more complex decoder. In particular, the decoder, which, when it is intended to distribute music, for example over the Internet, is a mass product, must be cost-effective in order to prevail over other encoders on the market.

At the same time, on the coding side, in the highly competitive market for audio coders, it is often intolerable to produce too much data, in other words, it is essential to achieve the highest possible compression factor, since there are often bandwidth-limited networks which result in an audio recording that is too lowly compressed having too long transmission time over such a network, which leads the customer to choose another product with higher data compression and thus a shorter transmission time.

The present invention is intended to provide an encoder/decoder design suitable for lossless encoding while providing high data compression at reasonable effort.

This task is solved by a process for processing time-discrete audio-sensory values according to claim 1, by a process for processing inverse integer values according to claim 17, by a device for processing time-discrete audio-sensory values according to claim 22 or by a device for processing inverse integer values according to claim 23.

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The rotation matrix is preferably a Givens rotation matrix, which is known to be represented by three lifting matrices. The rotation angle of the Givens rotation matrix depends on the window function. It should be noted that for the method of the invention all window functions are permitted, provided that these window functions satisfy the condition described that the square of a window weight and the square of a window weight spaced N times apart together give the value 1. It should be noted that this condition can also be satisfied by two consecutive windows of different shapes, such as a sinus window and a Kaiser-Bessel-fastener.

In a preferred embodiment of the present invention, the 50% overlap MDCT processing is replaced by lifting matrices and roundings and a subsequent discrete cosine transformation (DCT) with non-asymmetrical base functions, i.e. a DCT of type IV.

In order to achieve not only an integer window but also an integer discrete cosine transformation, it is also preferable to replace the DCT transformation by Givens rotations and in particular by processing with lifting matrices and rounding after each lifting matrix multiplication.

The present invention has the advantage that, either during the window or during the complete transformation, the starting values, i.e. the window sample values or the spectral values, remain integer. Nevertheless, the whole process is reversible by simply using the inverse rotations in reverse order with respect to the processing of the lifting matrices and the same rounding function.

The concept of the invention still has the advantageous characteristics of the MDCT, i.e. an overlapping structure which provides better frequency selectivity than non-overlapping block transformations and a critical sampling so that the total number of spectral values representing an audio signal does not exceed the number of input input values. Non-linearities are introduced due to the rounding in the rotational steps, but the roundings only lead to the simultaneous fact that the energy range of the total spectral values does not significantly exceed the energy range of the input values.

An advantage of the present invention is also that, because of the fact that integer inputs exist, subsequent quantization can be dispensed with, so that the inputs of the integer MDCT can be directly entropy-coded to obtain a lossless data compressor.

The following are examples of preferred embodiments of the present invention, which are described in detail in the accompanying drawings: Fig. 1a block diagram of a device according to the invention for processing time-discrete audio samples to obtain integer values;Fig. 2a schematic representation of the decomposition of an MDCT and an inverse MDCT into Givens rotations and two DCT-IV operations according to a preferred embodiment of the present invention;Fig. 3a diagram to illustrate the decomposition of the MDCT with 50-percent overlap into rotations and DCT-IV operations;Fig. 4a schematic block diagram of a known MDCT and 50 percent overlap encoder; andFig. 4a block diagram of a known decoder generated by decoding the output of Fig. 4a.

The time-discrete values are encoded by the device shown in Fig. 1 and optionally converted into a spectral representation. The time-discrete values, which are inserted into the device at an E 10 only, are encoded with a window w of a length corresponding to 2N time-discrete input values, in order to obtain at an output 12 integer-numbered encoded values, which are suitable for transformation and, in particular, for introducing the direction of reflection of 14F in a spectral representation of the output values of NDCT, which is produced by an NDCT output of 40 MDCT, which is the opposite of the output values of NDCT.

The time-discrete values are first selected in a device 16 for the window of time-discrete values, two time-discrete values are selected, which together constitute a vector of time-discrete values. One time-discrete value selected by device 16 is located in the first quarter of the window. The other time-discrete value is located in the second quarter of the window, as shown in Fig. 3. The vector produced by device 16 is now loaded with a rotational matrix of dimension 2 x 2, whereby this operation is not performed directly, but by means of several so-called lifting matrices.

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The vector is now multiplied by the third Lifting matrix, i.e. the Lifting matrix at the far right of the above equation, to obtain a first result vector. This is represented in Fig. 1 by a device 18. According to the invention, the first result vector is now rounded by any rounding function that represents the sum of the real numbers into the sum of the integers, as shown in Fig. 1. At the output of device 20, a rounded first result vector is obtained.The rounded second result vector is now fed into a device 26 to multiply it by the left-hand side of the above equation, i.e. the first lifting matrix, to obtain a third result vector, which is finally rounded by a device 28 to finally obtain 12 full-window samples at the output, which now, if a spectral representation of the same is desired, must be processed by the device 14 to obtain 30 full-spectral values at a spectral output.

Preferably, device 14 is run as an integer DCT or an integer DCT.

The discrete cosine transformation of type 4 (DCT-IV) with length N is given by the following equation:

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The following is a discussion of how the angle α of Givens rotation depends on the window function.

An MDCT with a window length of 2N can be reduced to a discrete cosine transformation of type IV with a length N. This is achieved by performing the TDAC operation explicitly in the time domain and then applying the DCT-IV. At a 50% overlap, the left half of the window for a block t overlaps the right half of the previous block, i.e. block t-1. The overlapping part of two successive blocks t-1 and t is pre-processed in the time domain, i.e. before the transformation, as follows, i.e. between input 10 and output 12 of Fig. 1:

The values indicated with the tilde are the values at output 12 of Fig. 1, while the x values indicated without tilde in the above equation are the values at input 10 or behind the device 16 to be selected.

The TDAC condition for the window function w has the following context: $\text{w}\text{(}\frac{\text{N}}{\text{2}}\text{+}\text{k}{\text{)}}^{\text{2}}\text{+}\text{w}\text{(}\frac{\text{N}}{\text{2}}\text{- 1 -}\text{k}{\text{)}}^{\text{2}}\text{= 1}$

For certain angles αk, k = 0, ..., N/2-1 this preprocessing in the time domain can be written as Givens rotation as performed.

The angle α of Givens rotation depends on the window function w as follows: $\text{α = arctan[w(N/2-1-k) / w(N/2 + k)]}$

It should be noted that any window functions w can be used as long as they meet this TDAC condition.

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When the first vector is processed as described above, a second vector is selected from the x ((N/2-1) and x ((N/2) samples, i.e. again a sample from the first quarter of the window and a sample from the second quarter of the window, and is processed by the algorithm described in Fig. 1.In particular, the integrated window scans of the second and third quarters are fed into a DCT. The integrated window scans of the first quarter of the window are processed into a preceding DCT-IV together with the integrated window scans of the fourth quarter of the preceding window. Similarly, the fourth quarter of the integrated window scans in Fig. 2 is fed into a DCT-IV transformation together with the first quarter of the next window. The mean DCT-IV transformation shown in Fig. 2 32 now provides N integrated spectral values y (n) to y (n) − 1 (n). These integrated spectral values can now be quantum-coded, for example, without the need for simple encoding.The device shall be capable of being used in a wide range of applications, including:

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The initial operation is performed according to the invention by an inverse Givens rotation, i.e. such that the blocks 26, 28 or 22, 24 or 18, 20 pass through in the opposite direction. This is shown more precisely by the second lifting matrix of equation 1. $\text{(}\text{x}\text{,}\text{y}\text{) ↦ (}\text{x}\text{,}\text{y}\text{+}\text{x}\text{sin α)}$

The values of x, y on the right hand side of equation 6 are integers, but this is not true for the value of x sin α. $\text{(}\text{x}\text{,y) ↦ (}\text{x}\text{,}\text{y}\text{+}\text{r}\text{(}\text{x}\text{sin α))}$ This operation is performed by Unit 24.

The inverse image (in the decoder) is defined as follows: $\text{(}\text{x}\text{',}\text{y}\text{') ↦ (}\text{x}\text{',}\text{y}\text{' -}\text{r}\text{(}\text{x'}\text{sin α))}$

The negative sign before the rounding operation shows that the integer approximation of the lifting step can be reversed without introducing an error. Applying this approximation to each of the three lifting steps results in an integer approximation of the Givens rotation. The rounded rotation (in the encoder) can be reversed (in the decoder) without introducing an error by running the inverse rounded lifting steps in reverse order, i.e. by decoding the algorithm in Figure 1 from top to bottom.

If the rounding function r is point-symmetric, the inverse rounded rotation is identical to the rounded rotation with angle -α and is as follows:

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In Figure 3 below, the breakdown of a typical MDCT with overlapping windows 40 to 46 is shown again. The windows 40 to 46 overlap by 50% each. For each window, Givens rotations are first performed within the first and second quarters of a window or within the third and fourth quarters of a window, as schematically shown by arrows 48.

The invention therefore decomposes the usual Givens rotation into Lifting matrices, which are executed sequentially, introducing a rounding step after each Lifting matrix multiplication, so that the floating-point numbers are rounded immediately after their origin, so that before each multiplication of a resulting vector by a Lifting matrix the resulting vector has only integers.

The output values are therefore always integer, with the preference to use integer inputs as well. This is not a restriction, since any PCM input values, for example, as stored on a CD, are integer values, whose range of values varies depending on bitwidth, i.e. depending on whether the time-discrete digital input values are 16-bit or 24-bit values.

The transformation according to the present invention provides integer starting values instead of floating-point values. It provides a perfect reconstruction so that no error is introduced when a forward and then a backward transformation is performed. The transformation is a substitute for the modified discrete cosine transformation according to a preferred embodiment of the present invention. However, other transformation processes can also be performed in integers as long as a breakdown into rotations and a breakdown of the rotations into lifting steps is possible.

The integer MDCT according to the present invention has most of the advantages of the MDCT. It has an overlapping structure, which gives better frequency selectivity than non-overlapping block transformations. Due to the TDAC function, which is already taken into account in the window before the transformation, critical sampling is maintained so that the total number of spectral values representing an audio signal is equal to the total number of input sampling values.

Compared with a normal MDCT which provides floating point values, the integer transformation of the invention shows that only in the spectral range where there is little signal level, noise is increased compared to the normal MDCT, while this noise increase is not noticeable at significant signal levels.

The invention's integer transformation provides a good spectral representation of the audio signal while remaining in the range of the whole numbers. When applied to tonal parts of an audio signal, this results in a good energy concentration. This allows an efficient lossless coding scheme to be constructed by simply cascading the invention's window/transformation shown in Fig. 1 with an entropy coder. In particular, stacked coding using escape values, as used in MPEG AACes, is advantageous for the present invention. It is preferred to decrease all values down to two to fit into a desired coding table, then decrease the specific value of the coding table.

Err1:Expecting ',' delimiter: line 1 column 415 (char 414)The first alternative, i.e. the open-loop predictor, is called TNS. Quantization after prediction leads to an adaptation of the resulting quantization noise to the temporal structure of the audio signal and therefore prevents forechos in psychoacoustic audio coders. For lossless audio coding, the second alternative, i.e. with a closed-loop predictor, is more suitable because closed-loop prediction allows an accurate reconstruction of the input signal. When this technique is applied to an inventive generated spectrum, a rounding must be performed step by step after each step of the prediction filter to accurately measure the entire range.

To exploit the redundancy between two channels for data reduction, a center-sided encoding can also be used losslessly when using a rounded rotation with an angle π/4. Compared to the alternative of calculating the sum and difference of the left and right channel of a stereo signal, rounded rotation has the advantage of energy conservation. The use of so-called joint stereo encoding techniques can be turned on or off for each band, as is also done in the standard MPEG AAC.

Claims (23)

1. Method for processing time-discrete sampled values representing an audio signal so as to obtain integer values, comprising the following steps:

   windowing the time-discrete sampled values with a window (w) with a length corresponding to 2N time-discrete sampled values so as to provide windowed time-discrete sampled values for a conversion of the time-discrete sampled values in a spectral representation by means of a transform which may generate N output values from N input values, with the windowing comprising the following sub-steps:

   selecting (16) a time-discrete sampled value from a quarter of the window and a time-discrete sampled value from another quarter of the window so as to obtain a vector of time-discrete sampled values;

   applying a square rotation matrix to the vector, the dimension of which coincides with the dimension of the vector, with the rotation matrix being adapted to be represented by a plurality of lifting matrices, with one lifting matrix only comprising one element which depends on the window (w) and is unequal to 1 or 0, with the sub-step of applying comprising the following sub-steps:

   multiplying (18) the vector by a lifting matrix so as to obtain a first result vector;

   rounding (20) a component of the first result vector with a rounding function (r) mapping a

   real number onto an integer number so as to obtain a rounded first result vector;

   sequentially carrying out the steps of multiplying (22) and rounding (24) with another lifting matrix until all lifting matrices have been processed so as to obtain a rotated vector comprising an integer windowed sampled value from the quarter of the window and an integer windowed sampled value from the other quarter of the window.
2. Method in accordance with claim 1, wherein the lifting matrices are 2 x 2 matrices and where a total of three lifting matrices are available per rotation matrix.
3. Method in accordance with claim 1 or 2, wherein the step of multiplying the vector or a rounded result vector is carried out by forming partial products and summing up the partial products, with the step of rounding being carried out with non-integer partial products before being summed up.
4. Method in accordance with one of the preceding claims, wherein the window comprises a number of 2N sampled values which is equal to a power of the basis 2.
5. Method in accordance with one of the preceding claims, wherein the rotation matrix is a Givens rotation matrix.
6. Method in accordance with one of the preceding steps, further comprising the following step:

   carrying out the step of windowing for all time-discrete sampled values of the remaining quarter of the window so as to obtain 2N filtered integer sampled values; and

   converting (14) N windowed integer sampled values in a spectral representation by an integer DCT for values with the filtered integer sampled values of the second quarter and the third quarter of the window so as to obtain N integer spectral values.
7. Method in accordance with claim 6, wherein the integer DCT is a DCT comprising non-symmetric basis functions.
8. Method in accordance with claim 7, wherein the DCT is a type-IV-DCT.
9. Method in accordance with one of claims 6 to 8, wherein the DCT is adapted to be decomposed into Givens rotation matrices and the same are again decomposable into lifting matrices, wherein, after each multiplication with a lifting matrix, a rounding step is carried out.
10. Method in accordance with one of the preceding claims, wherein the Givens rotation matrix has the following shape: wherein the lifting matrices comprise the following shape: wherein the angle α is defined as follows: $\text{α = arctan [w(N/2-1-k) / w (N/2 + k)]}$ with k being a time index of the time-discrete sampled values and running from 0 to 2N-1 and with w being a window function.
11. Method in accordance with one of the preceding claims, wherein the following condition is fulfilled for the window function w: $\text{w}{\left(\frac{\text{N}}{\text{2}}\text{+}\text{k}\right)}^{\text{2}}\text{+}\text{w}{\left(\frac{\text{N}}{\text{2}}\text{- 1 -}\text{k}\right)}^{\text{2}}\text{= 1}$
12. Method in accordance with claim 11, wherein the window is a sine window.
13. Method in accordance with one of the preceding claims, wherein the time-discrete sampled values are integers.
14. Method in accordance with claim 6, further comprising the following step:

    entropy-encoding of the integer spectral values so as to obtain an entropy-encoded version of the audio signal.
15. Method in accordance with claim 6, further comprising the step of quantizing the integer spectral values considering the psychoacoustic masking threshold so as to obtain quantized spectral values which are quantized such that the quantizing noise has been essentially masked.
16. Method in accordance with claim 6, further comprising the step of filtering the integer spectral values over the frequency by means of a predictor with a closed loop and the step of rounding of prediction errors.
17. Method for inverse processing of integer values having been generated by the method in accordance with claim 1, comprising the following steps:

    applying the rotated vector with a rotation matrix inverse to the rotation matrix, with the inverse rotation matrix being adjusted to be represented by a plurality of inverse lifting matrices, with an inverse lifting matrix only comprising one element depending on the window and being unequal to 1 or 0, with the step of applying comprising the following sub-steps:

    multiplying the rotated vector with an inverse lifting matrix being inverse to the lifting matrix which has been used when generating the integer values so as to obtain a first inverse result vector;

    rounding a component of the first inverse result vector with the rounding function so as to obtain a rounded first inverse result vector; and

    sequentially carrying out the steps of multiplying and rounding with further lifting matrices in an order which is inversed with respect to the order when generating the integer values so as to obtain an inversely processed vector which includes an integer time-discrete sampled value from a quarter of the window and an integer time-discrete sampled value from another quarter of the window.
18. Method in accordance with claim 17, wherein the integer values have been generated by the method in accordance with claim 2 and include integer spectral values and wherein, prior to the step of applying the rotated vector, the following step is carried out:

    converting the integer spectral values by an integer DCT inverse to the integer DCT into a time representation so as to obtain the rotated vector.
19. Method in accordance with claim 17 or 18, wherein the rounding function is point-symmetric and wherein the inverse lifting matrices are identical to the lifting matrices, but with a negative rotary angle.
20. Method in accordance with claim 18, wherein the integer DCT is a DCT derived from the DCT of the type IV.
21. Method in accordance with one of claims 17 to 20, wherein the inverse lifting matrices are identical to the corresponding lifting matrices, however, apart from subsidiary diagonal elements which are, in the inverse lifting matrices, negative as compared to the lifting matrices.
22. Apparatus for processing time-discrete sampled values representing an audio signal so as to obtain integer values, comprising:

    means for windowing the time-discrete sampled values with a window (w) having a length corresponding to two 2N time-discrete sampled values so as to provide windowed time-discrete sampled values for a conversion of the time-discrete sampled values in a spectral representation by means of a transform which may generate N output values from N input values, with the means for windowing comprising the following sub-features:

    means for selecting (16) a time-discrete sampled value from a quarter of the window and a time-discrete sampled value from another quarter of the window so as to obtain a vector of time-discrete sampled values;

    means for applying a square rotation matrix to the vector, the dimension of which coincides with the dimension of the vector, with the rotation matrix being adjusted to be represented by a plurality of lifting matrices, with one lifting matrix only comprising one element which depends on the window (w) and is unequal to 1 or 0, with a means for applying comprising the following sub-features:

    means for multiplying (18) the vector by a lifting matrix so as to obtain a first result vector;

    means for rounding (20) a component of the first result vector with a rounding function (r) mapping a real number to an integer number so as to obtain a rounded first result vector; and

    means for sequentially carrying out the steps of multiplying (22) and rounding (24) with another lifting matrix until all lifting matrices have been processed so as to obtain a rotated vector comprising an integer windowed sampled value from the quarter of the window and an integer windowed sampled value from another quarter of the window.
23. Apparatus for inverse processing of integer values having been generated by the apparatus in accordance with claim 22, comprising:

    means for applying the rotated vector with a rotation matrix inverse to the rotation matrix, with the inverse rotation matrix being adjusted to be represented by a plurality of inverse lifting matrices, with one inverse lifting matrix only comprising one element depending on the window and being unequal to 1 or 0, with the means for applying comprising the following sub-features:

    means for multiplying the rotated vector by an inverse lifting matrix being inverse to the lifting matrix which has been lastly used when generating the integer values so as to obtain a first inverse result vector;

    means for rounding a component' of the first inverse result vector with the rounding function so as to obtain a rounded first inverse result vector; and

    means for sequentially carrying out the multiplying and rounding with further lifting matrices in an order which is inverse with respect to the order when generating the integer values so as to obtain an inversely processed vector which includes an integer time-discrete sampled value from a quarter of the window and an integer time-discrete sampled value from another quarter of the window.